Finite Group DatabasebetaFinite Group Databasebeta| order | 18354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C19 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C19×D23 |
| unambiguous semidirect product | C23⋊(C2×C3×C7×C19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C19 | D23 |
| commutator, cosocle, hypocenter | C23 | C2×C3×C7×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C19×C23 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C3×C7×C19 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9177 |
5187 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D19×D23, C3×D7×C19×D23, C3×D23×D133, … |
| maximal normal subgroup of | C3×C7×D19×D23, C3×D7×C19×D23, C3×D23×D133, … |
| maximal quotient of | C3×C7×C19×Dic23, C2×C3×C7×C19×D23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18354, 6);